680 * Proceedings of the Pioyal Society 
13. When the radius of the globe is infinitely small, 
W = .... (40), 
where fi denotes one and a half times the volume of the globule, 
and q the undisturbed velocity of the fluid in its neighbourhood. 
This corresponds <to the formula which I gave twenty-five years 
ago for the force experienced by a small sphere (whether of 
ferromagnetic or diamagnetic non-crystalline substance) in virtue 
of the inductive influence which it experiences in a magnetic 
field. 5 ? 
14. By taking an infinite straight line for the core a simple but 
very important example is afforded. In this case, the undisturbed 
motion of the fluid is in circles having their centres in the core 
(or axis, as we may now call it), and their planes perpendicular to 
it. As is well known, the velocity of irrotational revolution round 
a straight axis is inversely proportional to distance from the axis. 
Hence the potential function W for the force experienced by an 
infinitesimal solid sphere in the fluid is inversely as the square of 
the distance of its centre from the axis, and therefore the force is 
inversely as the cube of the distance, and is towards the nearest 
point of the axis. Hence, when the globule moves in a plane 
perpendicular to the axis, it describes one or other of the forms of 
Cotesian spiralsf. If it be projected obliquely to the axis, the 
component velocity parallel to the axis will remain constant, and 
the other component will be unaffected by that one; so that the 
projection of the globule on the plane perpendicular to the axis 
will always describe the same Cotesian spiral as would be described 
were there no motion parallel to the axis. If the globule be left 
to itself in any position it will commence moving towards the axis 
as if attracted by a force varying inversely as the cube of the dis¬ 
tance. It is remarkable that it traverses at right angles an in¬ 
creasing liquid current without any applied force to prevent it 
* “ On the Forces Experienced by Small Spheres under Magnetic Influ¬ 
ence, and some of the Phenomena presented by Diamagnetic Substances ” 
{Cambridge and Dublin Mathematical Journal, 31 ag 1847); and “ Remarks on 
the Forces experienced by Inductively Magnetised Ferromagnetic or Diamag¬ 
netic Non-crystalline Substances ” [Phil. 3Iag. October 1850). Reprint of 
Papers on Electrostatics and Magnetism, §£ 684-668. Macmillan, 1872. 
f Tail and Steele’s “ Dynamics of a Particle,” £ 149 (15), 
